An Immune-Inspired Approach with Interval Allocation in Solving Multimodal Multi-Objective Optimization Problems with Local Pareto Sets

In practical engineering,multi-objective optimization often encounters situations where multiple Pareto sets(PS)in the decision space correspond to the same Pareto front(PF)in the objective space,known as Multi-Modal Multi-Objective Optimization Problems(MMOP).Locating multiple equivalent global PSs poses a significant challenge in real-world applications,especially considering the existence of local PSs.Effectively identifying and locating both global and local PSs is a major challenge.To tackle this issue,we introduce an immune-inspired reproduction strategy designed to produce more offspring in less crowded,promising regions and regulate the number of offspring in areas that have been thoroughly explored.This approach achieves a balanced trade-off between exploration and exploitation.Furthermore,we present an interval allocation strategy that adaptively assigns fitness levels to each antibody.This strategy ensures a broader survival margin for solutions in their initial stages and progressively amplifies the differences in individual fitness values as the population matures,thus fostering better population convergence.Additionally,we incorporate a multi-population mechanism that precisely manages each subpopulation through the interval allocation strategy,ensuring the preservation of both global and local PSs.Experimental results on 21 test problems,encompassing both global and local PSs,are compared with eight state-of-the-art multimodal multi-objective optimization algorithms.The results demonstrate the effectiveness of our proposed algorithm in simultaneously identifying global Pareto sets and locally high-quality PSs.

An Improved Artificial Rabbits Optimization Algorithm with Chaotic Local Search and Opposition-Based Learning for Engineering Problems and Its Applications in Breast Cancer Problem

Artificial rabbits optimization(ARO)is a recently proposed biology-based optimization algorithm inspired by the detour foraging and random hiding behavior of rabbits in nature.However,for solving optimization problems,the ARO algorithm shows slow convergence speed and can fall into local minima.To overcome these drawbacks,this paper proposes chaotic opposition-based learning ARO(COARO),an improved version of the ARO algorithm that incorporates opposition-based learning(OBL)and chaotic local search(CLS)techniques.By adding OBL to ARO,the convergence speed of the algorithm increases and it explores the search space better.Chaotic maps in CLS provide rapid convergence by scanning the search space efficiently,since their ergodicity and non-repetitive properties.The proposed COARO algorithm has been tested using thirty-three distinct benchmark functions.The outcomes have been compared with the most recent optimization algorithms.Additionally,the COARO algorithm’s problem-solving capabilities have been evaluated using six different engineering design problems and compared with various other algorithms.This study also introduces a binary variant of the continuous COARO algorithm,named BCOARO.The performance of BCOARO was evaluated on the breast cancer dataset.The effectiveness of BCOARO has been compared with different feature selection algorithms.The proposed BCOARO outperforms alternative algorithms,according to the findings obtained for real applications in terms of accuracy performance,and fitness value.Extensive experiments show that the COARO and BCOARO algorithms achieve promising results compared to other metaheuristic algorithms.

LOCAL REGULARITY RESULT FOR SOLUTIONS OF OBSTACLE PROBLEMS

This paper gives the local regularity result for solutions to obstacle problems of A-harmonic equation divA(x, ξu(x)) = 0, |A.(x,ξ)|≈|?|p-1, when 1 < p < n and the obstacle function (?)≥0.

A MESHLESS LOCAL PETROV-GALERKIN METHOD FOR GEOMETRICALLY NONLINEAR PROBLEMS

Nonlinear formulations of the meshless local Petrov-Galerkin （MLPG） method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficulties in the large deformation analysis. The essential boundary conditions in the present formulation axe imposed by a penalty method. An incremental and iterative solution procedure is used to solve geometrically nonlinear problems. Several examples are presented to demonstrate the effectiveness of the method in geometrically nonlinear problems analysis. Numerical results show that the MLPG method is an effective one and that the values of the unknown variable are quite accurate.

Virtual local target method for avoiding local minimum in potential field based robot navigation

A novel robot navigation algorithm with global path generation capability is presented. Local minimum is a most intractable but is an encountered frequently problem in potential field based robot navigation.Through appointing appropriately some virtual local targets on the journey, it can be solved effectively. The key concept employed in this algorithm are the rules that govern when and how to appoint these virtual local targets. When the robot finds itself in danger of local minimum, a virtual local target is appointed to replace the global goal temporarily according to the rules. After the virtual target is reached, the robot continues on its journey by heading towards the global goal. The algorithm prevents the robot from running into local minima anymore. Simulation results showed that it is very effective in complex obstacle environments.

LOCAL EXISTENCE OF SOLUTION TO FREE BOUNDARY VALUE PROBLEM FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS

This paper is concerned with the free boundary value problem for multidimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. Local （in time） existence of a weak solution is established; in particular, the density is positive and the solution is regular away from the free boundary.

Locally Minimum Storage Regenerating Codes in Distributed Cloud Storage Systems

In distributed cloud storage systems, inevitably there exist multiple node failures at the same time. The existing methods of regenerating codes, including minimum storage regenerating(MSR) codes and minimum bandwidth regenerating(MBR) codes, are mainly to repair one single or several failed nodes, unable to meet the repair need of distributed cloud storage systems. In this paper, we present locally minimum storage regenerating(LMSR) codes to recover multiple failed nodes at the same time. Specifically, the nodes in distributed cloud storage systems are divided into multiple local groups, and in each local group(4, 2) or(5, 3) MSR codes are constructed. Moreover, the grouping method of storage nodes and the repairing process of failed nodes in local groups are studied. Theoretical analysis shows that LMSR codes can achieve the same storage overhead as MSR codes. Furthermore, we verify by means of simulation that, compared with MSR codes, LMSR codes can reduce the repair bandwidth and disk I/O overhead effectively.

ON TRANSMISSION PROBLEM FOR KIRCHHOFF TYPE WAVE EQUATION WITH A LOCALIZED NONLINEAR DISSIPATION IN BOUNDED DOMAIN

In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physi- cally different types of materials, one component is a Kirchhoff type wave equation with nonlinear time dependent localized dissipation which is effective only on a neighborhood of certain part of the boundary, while the other is a Kirchhoff type wave equation with nonlinear memory.

SOLVING MINIMUM SPANNING TREE PROBLEM WITH DNA COMPUTING

Molecular programming is applied to minimum spanning problem whose solution requires encoding of real values in DNA strands. A new encoding scheme is proposed for real values that is biologically plausible and has a fixed code length. According to the characteristics of the problem, a DNA algorithm solving the minimum spanning tree problem is given. The effectiveness of the proposed method is verified by simulation. The advantages and disadvantages of this algorithm are discussed.

LOCAL REGULARITY RESULT IN OBSTACLE PROBLEMS

We obtain a local regularity result for solutions to kφ,θ-obstacle problem of A-harmonic equation divA（x, u（x）, ↓△u（x）） = 0, where .A ： Ω ×R × Rn → Rn is aCarath^odory function satisfying some coercivity and growth conditions with the naturalexponent 1 〈 p 〈 n, the obstacle function φ≥ 0, and the boundary data θ ∈ W1mp（Ω）.

Source localization with minimum variance distortionless response for spherical microphone arrays

To improve localization accuracy, the spherical microphone arrays are used to capture high-order wavefield in- formation. For the far field sound sources, the array signal model is constructed based on plane wave decomposition. The spatial spectrum function is calculated by minimum variance distortionless response （MVDR） to scan the three-dimensional space. The peak values of the spectrum function correspond to the directions of multiple sound sources. A diagonal loading method is adopted to solve the ill-conditioned cross spectrum matrix of the received signals. The loading level depends on the alleviation of the ill-condition of the matrix and the accuracy of the inverse calculation. Compared with plane wave decomposition method, our proposed localization algorithm can acquire high spatial resolution and better estimation for multiple sound source directions, especially in low signal to noise ratio （SNR）.

A GLOBAL LINEAR AND LOCAL QUADRATIC SINGLE-STEP NONINTERIOR CONTINUATION METHOD FOR MONOTONE SEMIDEFINITE COMPLEMENTARITY PROBLEMS

A noninterior continuation method is proposed for semidefinite complementarity problem （SDCP）. This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main properties of our method are： （i） it is well d.efined for the monotones SDCP; （ii） it has to solve just one linear system of equations at each step; （iii） it is shown to be both globally linearly convergent and locally quadratically convergent under suitable assumptions.

The complex variable meshless local Petrov-Galerkin method of solving two-dimensional potential problems

Based on the complex variable moving least-square（CVMLS） approximation and a local symmetric weak form,the complex variable meshless local Petrov-Galerkin（CVMLPG） method of solving two-dimensional potential problems is presented in this paper.In the present formulation,the trial function of a two-dimensional problem is formed with a one-dimensional basis function.The number of unknown coefficients in the trial function of the CVMLS approximation is less than that in the trial function of the moving least-square（MLS） approximation.The essential boundary conditions are imposed by the penalty method.The main advantage of this approach over the conventional meshless local Petrov-Galerkin（MLPG） method is its computational efficiency.Several numerical examples are presented to illustrate the implementation and performance of the present CVMLPG method.

Exact Algorithm to Solve the Minimum Cost Multi-Constrained Multicast Routing Problem

The optimal solution of the multi-constrained QoS multicast routing problem is a tree-like hierarchical structure in the topology graph. This multicast route contains a feasible path from the source node to each of the destinations with respect to a set of QoS constraints while minimizing a cost function. Often, it is a tree. In other cases, the hierarchies can return several times to nodes and links of the topology graph. Similarly to Steiner problem, finding such a structure is an NP-hard problem. The usual tree and topology enumeration algorithms applied for the Steiner problem cannot be used to solve the addressed problem. In this paper, we propose an exact algorithm based on the Branch and Bound principle and improved by the Lookahead technique. We show relevant properties of the optimum hierarchy permitting efficient pruning of the search space. To our knowledge, our paper is the first to propose an exact algorithm for this non-trivial multi-constrained optimal multicast route computation. Simulations illustrate the efficiency of the proposed pruning operations. The analysis of the execution time shows that in simple topologies and with tight QoS constraints the exact algorithm requires relatively little execution time. With loose constraints the computation time cannot be tolerated even for off-line route computation. In these cases, the solution is close to a Steiner tree and heuristics can be applied. These results can serve as basis for the design of efficient, polynomial-time routing algorithms.

ON TRANSMISSION PROBLEM FOR VISCOELASTIC WAVE EQUATION WITH A LOCALIZED A NONLINEAR DISSIPATION

In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physically different types of materials, one component being a Kirchhoff type wave equation with time dependent localized dissipation which is effective only on a neighborhood of certain part of boundary, while the other being a Kirchhoff type viscoelastic wave equation with nonlinear memory

LOCAL DISCONTINUOUS GALERKIN METHOD FOR ELLIPTIC INTERFACE PROBLEMS

In this paper,the minimal dissipation local discontinuous Galerkin method is studied to solve the elliptic interface problems in two-dimensional domains.The interface may be arbitrary smooth curves.It is shown that the error estimates in L;-norm for the solution and the flux are O（h;|log h|）and O(h|log h|;),respectively.In numerical experiments,the successive substitution iterative methods are used to solve the LDG schemes.Numerical results verify the efficiency and accuracy of the method.

A Multiple-Neighborhood-Based Parallel Composite Local Search Algorithm for Timetable Problem

This paper presents a parallel composite local search algorithm based on multiple search neighborhoods to solve a special kind of timetable problem. The new algorithm can also effectively solve those problems that can be solved by general local search algorithms. Experimental results show that the new algorithm can generate better solutions than general local search algorithms.

GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMSIN LOCALLY G-CONVEX SPACES

Some classes of generalized vector quasi-equilibrium problems ( in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems; generalized vector variational inequality problems, quasi-equilibrium problems and quasi-variational inequality problems as special cases. First, an equilibrium existence theorem for one person games is proved in locally G-convex spaces.. As applications, some new existence theorems of solutions for the GVQEP are established in noncompact locally G-convex spaces. These results and argument methods are new and completely different from that in recent literature.

Bottleneck Analysis of the Minimum Cost Problem for the Generalized Network Based on Augmented Forest Structure

The bottleneck analysis of the minimum cost problem for the generalized network (MCPGN) is discussed. The analysis is based on the network simplex algorithm, which gains negative cost graphs by constructing augmented forest structure, then augments flows on the negative cost graphs until the optimal revolution is gained. Bottleneck structure is presented after analyzing the augmented forest structure. The negative cost augmented graphs are constructed with the bottleneck structure. The arcs that block the negative cost augmented graph are the elements of the bottleneck. The bottleneck analysis for the generalized circulation problem, the minimum circulation problem and the circulation problem are discussed respectively as the basal problems, then that for MCPGN is achieved. An example is presented at the end.

LOCAL SOLVABILITY OF THE CAUCHY PROBLEM OF A FIFTH-ORDER NONLINEAR DISPERSIVE EQUATION

The solvability of the fifth-order nonlinear dispersive equation δtu＋au （δxu）^2＋βδx^3u＋γδx^5u = 0 is studied. By using the approach of Kenig, Ponce and Vega and some Strichartz estimates for the corresponding linear problem,it is proved that if the initial function u0 belongs to H^5（R） and s〉1/4,then the Cauchy problem has a unique solution in C（[-T,T],H^5（R）） for some T〉0.